Decibel (Db) : It is a unit of the relative measurement of the vibration and sound. It is defined in terms of a power ratio:
where p is the power, since power is proportion to square of amplitude of vibrations or voltages, which is easily measurable, hence
(1.6)
where A is the amplitude. For amplitude gain of 5, the decibel has a gain of
(1.7)
In vibrations decibel is used to express relative measured values of displacements, velocities and accelerations.
(1.8)